GATE 2021 CH – Question 47
Formaldehyde is produced by the oxidation of methane in a reactor. The following two parallel reactions occur: $\mathrm{CH_4+O_2\to HCHO+H_2O}$ and $\mathrm{CH_4+2O_2\to CO_2+2H_2O}$. Methane and oxygen are fed to the reactor. The product gases leaving the reactor include methane, oxygen, formaldehyde, carbon dioxide and water vapor. $60\ \mathrm{mol\,s^{-1}}$ of methane enters the reactor. The molar flowrate (in $\mathrm{mol\,s^{-1}}$) of $\mathrm{CH_4,O_2}$ and $\mathrm{CO_2}$ leaving the reactor are 26, 2 and 4, respectively. The molar flowrate of oxygen entering the reactor is _____.
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Correct answer: 40
Explanation
Total methane consumed is $60-26=34\ \mathrm{mol\,s^{-1}}$. Each mole of carbon dioxide corresponds to one mole of methane consumed by complete oxidation, so the second reaction has extent $4\ \mathrm{mol\,s^{-1}}$.
The first reaction therefore consumes $34-4=30\ \mathrm{mol\,s^{-1}}$ of methane. Oxygen consumption is $30(1)+4(2)=38\ \mathrm{mol\,s^{-1}}$. Adding the 2 mol/s of unreacted oxygen leaving gives an inlet oxygen flow of $38+2=\mathbf{40\ \mathrm{mol\,s^{-1}}}$.